Acoustic shock waves are used to break up concretions in the human body, to treat soft-tissue complaints, to stimulate the nerves, and to treat bone diseases. Devices for generating such acoustic shock waves are known from, for example, EP 0,590,177 A1 and WO 96/09,621. In these devices, an electrical spark discharge is generated between two electrodes in a fluid. The spark discharge causes shock waves to form in the fluid, which are focussed by a reflector on the target area to be treated. To conduct the shock waves generated in the volume of fluid into the tissues of the human body, the fluid volume is closed off by an exciting membrane, which is brought into contact with the surface of the human body. Because the spark discharge is always associated with the loss of material from the electrodes, the electrodes have only a relatively short service life. In the known devices, the electrodes are therefore mounted in the fluid volume enclosed by the exciting membrane in such a way that they can be replaced. The fluid volume is connected to a circulation system, through which the fluid is circulated and where it is processed, that is, heated, filtered, and degassed. The circulation system and the connection of the fluid volume to the circulation system are complicated assemblies and occupy a considerable amount of space. Replacing the electrodes is therefore time consuming and makes it necessary to open up the fluid volume and the circulation system.